test/verify/aoj-cgl-7-h.test.cpp

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• Last update: 2024-04-27 01:27:28+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H

Depends on

• geometry/base.hpp
• geometry/ccw.hpp
• geometry/circle.hpp
• geometry/common_area_cp.hpp
• geometry/cross_point_cl.hpp
• geometry/distance_sp.hpp
• geometry/is_intersect_cs.hpp
• geometry/is_intersect_sp.hpp
• geometry/line.hpp
• geometry/point.hpp
• geometry/polygon.hpp
• geometry/projection.hpp
• geometry/segment.hpp
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
// competitive-verifier: ERROR 0.00001

#include "../../template/template.hpp"

#include "../../geometry/common_area_cp.hpp"

using namespace geometry;

int main() {
  int N;
  Real R;
  cin >> N >> R;
  Circle c(Point(0, 0), R);
  Polygon p(N);
  for(auto &s : p) cin >> s;
  cout << common_area_cp(c, p) << endl;
}

#line 1 "test/verify/aoj-cgl-7-h.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
// competitive-verifier: ERROR 0.00001

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 5 "test/verify/aoj-cgl-7-h.test.cpp"

#line 2 "geometry/base.hpp"

namespace geometry {
using Real = double;
const Real EPS = 1e-8;
const Real PI = acos(static_cast<Real>(-1));

enum { OUT, ON, IN };

inline int sign(const Real &r) { return r <= -EPS ? -1 : r >= EPS ? 1 : 0; }

inline bool equals(const Real &a, const Real &b) { return sign(a - b) == 0; }
}  // namespace geometry
#line 3 "geometry/point.hpp"

namespace geometry {
using Point = complex<Real>;

istream &operator>>(istream &is, Point &p) {
  Real a, b;
  is >> a >> b;
  p = Point(a, b);
  return is;
}

ostream &operator<<(ostream &os, const Point &p) {
  return os << real(p) << " " << imag(p);
}

Point operator*(const Point &p, const Real &d) {
  return Point(real(p) * d, imag(p) * d);
}

// rotate point p counterclockwise by theta rad
Point rotate(Real theta, const Point &p) {
  return Point(cos(theta) * real(p) - sin(theta) * imag(p),
               sin(theta) * real(p) + cos(theta) * imag(p));
}

Real cross(const Point &a, const Point &b) {
  return real(a) * imag(b) - imag(a) * real(b);
}

Real dot(const Point &a, const Point &b) {
  return real(a) * real(b) + imag(a) * imag(b);
}

bool compare_x(const Point &a, const Point &b) {
  return equals(real(a), real(b)) ? imag(a) < imag(b) : real(a) < real(b);
}

bool compare_y(const Point &a, const Point &b) {
  return equals(imag(a), imag(b)) ? real(a) < real(b) : imag(a) < imag(b);
}

using Points = vector<Point>;
}  // namespace geometry
#line 3 "geometry/circle.hpp"

namespace geometry {
struct Circle {
  Point p;
  Real r{};

  Circle() = default;

  Circle(const Point &p, const Real &r) : p(p), r(r) {}
};

using Circles = vector<Circle>;
}  // namespace geometry
#line 3 "geometry/line.hpp"

namespace geometry {
struct Line {
  Point a, b;

  Line() = default;

  Line(const Point &a, const Point &b) : a(a), b(b) {}

  Line(const Real &A, const Real &B, const Real &C) {  // Ax+By=C
    if (equals(A, 0)) {
      assert(!equals(B, 0));
      a = Point(0, C / B);
      b = Point(1, C / B);
    } else if (equals(B, 0)) {
      a = Point(C / A, 0);
      b = Point(C / A, 1);
    } else {
      a = Point(0, C / B);
      b = Point(C / A, 0);
    }
  }

  friend ostream &operator<<(ostream &os, Line &l) {
    return os << l.a << " to " << l.b;
  }

  friend istream &operator>>(istream &is, Line &l) { return is >> l.a >> l.b; }
};

using Lines = vector<Line>;
}  // namespace geometry
#line 2 "geometry/projection.hpp"

#line 5 "geometry/projection.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_A
Point projection(const Line &l, const Point &p) {
  auto t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + (l.a - l.b) * t;
}
}  // namespace geometry
#line 6 "geometry/cross_point_cl.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_D
Points cross_point_cl(const Circle &c, const Line &l) {
  Point pr = projection(l, c.p);
  if (equals(abs(pr - c.p), c.r)) return {pr};
  Point e = (l.b - l.a) / abs(l.b - l.a);
  auto k = sqrt(norm(c.r) - norm(pr - c.p));
  return {pr - e * k, pr + e * k};
}
}  // namespace geometry
#line 3 "geometry/ccw.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
constexpr int COUNTER_CLOCKWISE = +1;
constexpr int CLOCKWISE = -1;
constexpr int ONLINE_BACK = +2;   // c-a-b
constexpr int ONLINE_FRONT = -2;  // a-b-c
constexpr int ON_SEGMENT = 0;     // a-c-b
int ccw(const Point &a, Point b, Point c) {
  b = b - a, c = c - a;
  if (sign(cross(b, c)) == +1) return COUNTER_CLOCKWISE;
  if (sign(cross(b, c)) == -1) return CLOCKWISE;
  if (sign(dot(b, c)) == -1) return ONLINE_BACK;
  if (norm(b) < norm(c)) return ONLINE_FRONT;
  return ON_SEGMENT;
}
}  // namespace geometry
#line 3 "geometry/segment.hpp"

namespace geometry {
struct Segment : Line {
  Segment() = default;

  using Line::Line;
};

using Segments = vector<Segment>;
}  // namespace geometry
#line 4 "geometry/is_intersect_sp.hpp"

namespace geometry {
bool is_intersect_sp(const Segment &s, const Point &p) {
  return ccw(s.a, s.b, p) == ON_SEGMENT;
}
}  // namespace geometry
#line 5 "geometry/distance_sp.hpp"

namespace geometry {
Real distance_sp(const Segment &s, const Point &p) {
  Point r = projection(s, p);
  if (is_intersect_sp(s, r)) return abs(r - p);
  return min(abs(s.a - p), abs(s.b - p));
}
}  // namespace geometry
#line 6 "geometry/is_intersect_cs.hpp"

namespace geometry {
int is_intersect_cs(const Circle &c, const Segment &l) {
  Point h = projection(l, c.p);
  if (sign(norm(h - c.p) - norm(c.r)) > 0) return 0;
  auto d1 = abs(c.p - l.a), d2 = abs(c.p - l.b);
  if (sign(c.r - d1) >= 0 && sign(c.r - d2) >= 0) return 0;
  if (sign(c.r - d1) < 0 && sign(d2 - c.r) > 0 ||
      sign(d1 - c.r) > 0 && sign(c.r - d2) < 0)
    return 1;
  if (sign(dot(l.a - h, l.b - h)) < 0) return 2;
  return 0;
}
}  // namespace geometry
#line 2 "geometry/polygon.hpp"

#line 4 "geometry/polygon.hpp"

namespace geometry {
using Polygon = vector<Point>;
using Polygons = vector<Polygon>;
}  // namespace geometry
#line 7 "geometry/common_area_cp.hpp"

namespace geometry {
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_H
Real ca_cp_impl(const Circle &c, const Point &a, const Point &b) {
  auto va = c.p - a, vb = c.p - b;
  Real f = cross(va, vb), ret = 0;
  if (sign(f) == 0) return ret;
  if (sign(max(abs(va), abs(vb)) - c.r) <= 0) return f;
  if (sign(distance_sp(Segment(a, b), c.p) - c.r) >= 0)
    return norm(c.r) * arg(vb * conj(va));
  auto tot = cross_point_cl(c, Line(a, b));
  if (is_intersect_cs(c, Segment(a, b)) != 2 and
      dot(a - tot[0], b - tot[0]) < 0) {
    swap(tot[0], tot[1]);
  }
  tot.emplace(begin(tot), a);
  tot.emplace_back(b);
  for (int i = 1; i < (int)tot.size(); i++) {
    ret += ca_cp_impl(c, tot[i - 1], tot[i]);
  }
  return ret;
}

Real common_area_cp(const Circle &c, const Polygon &p) {
  if (p.size() < 3) return 0;
  Real A = 0;
  for (int i = 0; i < p.size(); i++) {
    A += ca_cp_impl(c, p[i], p[(i + 1) % p.size()]);
  }
  return A * 0.5;
}
}  // namespace geometry
#line 7 "test/verify/aoj-cgl-7-h.test.cpp"

using namespace geometry;

int main() {
  int N;
  Real R;
  cin >> N >> R;
  Circle c(Point(0, 0), R);
  Polygon p(N);
  for(auto &s : p) cin >> s;
  cout << common_area_cp(c, p) << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00.in	AC	6 ms	4 MB
g++	00_sample_01.in	AC	6 ms	4 MB
g++	01_triangle_00.in	AC	6 ms	4 MB
g++	01_triangle_01.in	AC	6 ms	4 MB
g++	01_triangle_02.in	AC	6 ms	4 MB
g++	01_triangle_03.in	AC	6 ms	4 MB
g++	01_triangle_04.in	AC	6 ms	4 MB
g++	01_triangle_05.in	AC	6 ms	4 MB
g++	01_triangle_06.in	AC	6 ms	4 MB
g++	01_triangle_07.in	AC	6 ms	4 MB
g++	02_small_00.in	AC	6 ms	4 MB
g++	02_small_01.in	AC	6 ms	4 MB
g++	02_small_02.in	AC	6 ms	4 MB
g++	03_medium_00.in	AC	6 ms	4 MB
g++	03_medium_01.in	AC	6 ms	4 MB
g++	04_corner_00.in	AC	8 ms	4 MB
g++	04_corner_01.in	AC	6 ms	4 MB
g++	04_corner_02.in	AC	6 ms	4 MB
g++	04_corner_03.in	AC	7 ms	4 MB
g++	04_corner_04.in	AC	7 ms	4 MB
g++	05_corner_00.in	AC	6 ms	4 MB
g++	05_corner_01.in	AC	6 ms	4 MB
g++	05_corner_02.in	AC	6 ms	4 MB
g++	05_corner_03.in	AC	6 ms	4 MB
g++	05_corner_04.in	AC	6 ms	4 MB
g++	05_corner_05.in	AC	6 ms	4 MB
g++	05_corner_06.in	AC	6 ms	4 MB
g++	05_corner_07.in	AC	6 ms	4 MB
g++	06_maximum_00.in	AC	6 ms	4 MB
g++	06_maximum_01.in	AC	6 ms	4 MB
g++	06_maximum_02.in	AC	6 ms	4 MB
g++	06_maximum_03.in	AC	6 ms	4 MB
clang++	00_sample_00.in	AC	6 ms	4 MB
clang++	00_sample_01.in	AC	6 ms	4 MB
clang++	01_triangle_00.in	AC	6 ms	4 MB
clang++	01_triangle_01.in	AC	6 ms	4 MB
clang++	01_triangle_02.in	AC	7 ms	4 MB
clang++	01_triangle_03.in	AC	6 ms	4 MB
clang++	01_triangle_04.in	AC	6 ms	4 MB
clang++	01_triangle_05.in	AC	6 ms	4 MB
clang++	01_triangle_06.in	AC	6 ms	4 MB
clang++	01_triangle_07.in	AC	6 ms	4 MB
clang++	02_small_00.in	AC	6 ms	4 MB
clang++	02_small_01.in	AC	6 ms	4 MB
clang++	02_small_02.in	AC	6 ms	4 MB
clang++	03_medium_00.in	AC	6 ms	4 MB
clang++	03_medium_01.in	AC	6 ms	4 MB
clang++	04_corner_00.in	AC	6 ms	4 MB
clang++	04_corner_01.in	AC	6 ms	4 MB
clang++	04_corner_02.in	AC	7 ms	4 MB
clang++	04_corner_03.in	AC	6 ms	4 MB
clang++	04_corner_04.in	AC	6 ms	4 MB
clang++	05_corner_00.in	AC	6 ms	4 MB
clang++	05_corner_01.in	AC	6 ms	4 MB
clang++	05_corner_02.in	AC	6 ms	4 MB
clang++	05_corner_03.in	AC	6 ms	4 MB
clang++	05_corner_04.in	AC	6 ms	4 MB
clang++	05_corner_05.in	AC	6 ms	4 MB
clang++	05_corner_06.in	AC	6 ms	4 MB
clang++	05_corner_07.in	AC	6 ms	4 MB
clang++	06_maximum_00.in	AC	6 ms	4 MB
clang++	06_maximum_01.in	AC	6 ms	4 MB
clang++	06_maximum_02.in	AC	6 ms	4 MB
clang++	06_maximum_03.in	AC	6 ms	4 MB

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